Question

Using the following data, test the question that an equal number of Democrats, Republicans, and the Independents voted during the most recent election. Test this hypothesis at the .05 level of significance.

Political Affiliation
Republican	Democrat	Independent
800	700	900

Answer 1

null hypothesis:Ho:  equal number of Democrats, Republicans, and the Independents voted during the most recent election.

alternate hypothesis:Ha:not all three categories have equal proportion of votes during the most recent election.

degree of freedom =categories-1=

2

for 0.05 level and 2 degree of freedom :rejection region =

5.991

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
republican	0.333	800	800.00	0.00	0.000
Democrat	0.333	700	800.00	-3.54	12.500
Independent	0.333	900	800.00	3.54	12.500
total	1.000	2400	2400		25.000

test statistic X² =25.00

as test statistic is higher then critical value; we reject null hypothesis

we have sufficient evidence at 0.05 level to conclude that not all three categories have equal proportion of votes during the most recent election.